Apparently she had visited her daughters house and decided not to stay, instead she slept in her car. In the morning she found she had a flat battery from leaving the heater on. At this point the police turned up and she asked if they had any jump leads to start her car, they then arrested her for failing to provide a breath test.
So let's dissect this down. First of all there's nothing wrong with sleeping in your vehicle, in fact if you do feel tired finding a safe point and taking a nap is a government recommended action. Having a flat battery is also not an offence, nor is asking for jump leads. Failing to provide a breath test though is an offence however it can only be requested under specific circumstances.

the police officer has reasonable cause to suspect that you have committed, or are currently committing a moving traffic offence, or

if, having stopped, an officer has reasonable cause to suspect that the person driving/attempting to drive/in charge of the vehicle has consumed alcohol, or

the police officer has reasonable cause to believe that you were the person driving/attempting to drive/in charge of a motor vehicle which was involved in an accident.

So which applies here? No moving offence as the vehicle wasn't moving so not 1. No thought of an accident occurring so not 3, which leaves us with option 2 - suspicion.

Let's pare down number 2- first off reasonable cause the incident wasn't filmed so it's impossible to comment directly on any actions that might have caused suspicion in the officers. Next driving/attempting to drive/in charge of vehicle. Well not driving, but as she asked for jump leads attempting to drive can be placed as a fair conclusion; likewise being the only person there she was in charge of the vehicle (more on that later). So with that conclusion the request was legitimate.

That is until the charge was dropped. At this point we have a problem that extends beyond the physical assault. Remember she wasn't charged with any drink driving offence she was charged for failing to provide a breath test that was supposedly asked of her under legitimate circumstances those being reasonable cause that a) she was in charge of the vehicle and b) she had consumed alcohol.

Now the charge should only have been dropped if she provided a breath test at the roadside (any provided at the station does not counter this offence) or if there was no reasonable cause. In which case why was she arrested in the first place? A suggestion is made that she was swearing, which can be considered an offence however this was not what she was charged with and is therefore irrelevant.

As an aside remember the police are simply citizens with extended powers you are not obliged to obey the instruction of any officer acting unlawfully though you'd better have a damn good knowledge of the law in question before you start an argument.

Okay off track I mentioned "in charge of a vehicle" this is another delightful bit of verbiage embedded within our laws that has no definition beyond that set by precedent. Do you have the keys to the car in your pocket, are you near the car in question? Congratulations you are now considered "in charge" of said car under the law.

What that means is that if you come out of the pub totally pissed with your car keys in your pocket and walk past your car, under the second proviso above the police can ask you to provide a breath test and should you prove positive you can get a 3 month sentence or a fine of up to £2500, and ten points. It's not up to the police to prove you were going to use your vehicle; it's up to you to prove you weren't.

In reality they'd probably wait until you tried to access the vehicle and drive off; but technically they don't have to. Neat eh?